Quadratic Sparse Domination and Weighted Estimates for Non-integral Square Functions

Abstract We prove a quadratic sparse domination result for general non-integral square functions S . That is, $$p_0 \in [1,2)$$ p 0 ∈ [ 1 , 2 ) and $$q_0 (2,\infty ]$$ q ( ∞ ] , we an estimate of the form "Equation missing"where $$q_{0}^{*}$$ ∗ is Hölder conjugate $$q_{0}/2$$ / M underlying doubling space $${\mathcal {S}}$$ S collection cubes on Our will cover both associated with divergence elliptic operators those Laplace–Beltrami operator. This allows us to derive optimal norm estimates in weighted $$L^{p}(w)$$ L w